More precisely, in this paper, we present two reformulations of the general sparse optimization problem REF .
These reformulations are introduced in Section , and partially motivated by a related approach from [1]}, [2]} for cardinality-constrained optimization problems, cf. the corresponding discussion in Section .
One of the two reformulations is exactly the one from [3]} that we already mentioned previously.
Note that the subsequent results shown for our two reformulated problems are even new for the
approach from [3]}.
In particular, we verify in Section  that problem REF  and our two reformulations
are equivalent in terms of both local and global minima.
Section  introduces a problem-tailored strong stationarity concept and a corresponding
constraint qualification and shows that these correspond to the standard KKT conditions and a standard constraint qualification of the two reformulated problems.
We then discuss suitably adapted second-order conditions in Section .
